3 Answers
3

Damaging an altar (either with bombs or by enemies/traps while you're in the level) will result in punishments:

Damage an altar once and you will get a lot of spiders after you.

Damage once twice and you'll also get a ball a chain that you have to drag around the level.

Damage one a third time and the level will also go dark and a ghost will be summoned. Unless you're right next to an exit you are unlikely survive this.

Sacrifice items to an altar to get rewards:

Drop a gold idol to get a golden monkey that runs around the level crapping gold. I think this might eventually net more gold than the idol would have given you, but it's hard keeping the monkey alive.

Drop a stunned (or dead) enemy to please Kali a little.

Drop a stunned damsel to please Kali a lot - one damsel is enough for a random item reward.

Please Kali enough and you get the Kapala - a skull cup that gives you back health from bleeding enemies.

As an amusing bit of trivia, accidentally sacrificing yourself on the altar (falling or being knocked onto one while stunned) also seems to please Kali equally to a damsel; every time it's happened to me, a random item reward has spawned.
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cloudymusicJul 19 '12 at 16:05

In the original Spelunky they were all the things were worth sacrifice points, I believe the Stunned Damsel/Idol were 8 (if dead the damsel is worth 1 or 2, the same goes for regular enemies, alive they are 2, dead they are 1) I have a feeling a stunned Shopkeeper is also worth 8, at 8 sacrifice points Kali gives you a random item, at 16 (2 damsels) you get the Kapala, I think at 32 (4 damsels) you get an extra 8 lives, I believe the Throne in the Black Knights castle acts as a regular altar.